Transversely Isotropic Failure Surface

Introduction

This damage initiation law predicts failure in transversely isotropic materials. Because it deals with a specific material type, this law is only appropriate for TransIsoSoftening materials.

Failure Surface

This failure surface has five failure properties. First, are two tensile strengths [math]\displaystyle{ \sigma_A }[/math] and [math]\displaystyle{ \sigma_T }[/math]. The first tensile strength is for tensile loading in the axial direction. The second is for tensile failure in the isotropic plane, which occurs in the maximum normal stress direction in that plane.

Second, are three shear strengths [math]\displaystyle{ \tau_A }[/math], [math]\displaystyle{ \tau_T }[/math], and [math]\displaystyle{ \tau_{RS} }[/math]. The first two shear strength are for failure at maximum shear stress in planes parallel to the axial direction. When failure occurs in such a plane, the resulting crack will either be parallel to the axial direction with normal in transverse direction (if [math]\displaystyle{ \tau_A \lt \tau_T }[/math]) or parallel to the transverse direction with normal in the axial direction (if [math]\displaystyle{ \tau_T\lt \tau_A }[/math]) . The last shear strength is for failure in the isotropic plane, which occurs in the maximum shear stress direction in that plane.

Damage Law Properties

The following table lists the input properties for this initiation law

Property	Description	Units	Default
sigmacA	Critical stress for failure in the axial direction (output as sigcA)	pressure units	infinite
sigmac	Critical transverse tensile strength for tensile failure in the isotropic plane (output as sigcT)	pressure units	infinite
taucA	Critical shear stress for failure due to axial shear stress with failure parallel to the axial direction	pressure units	infinite
taucT	Critical shear stress for failure due to axial shear stress with failure through the axial direction	pressure units	infinite
tauc	Critical transverse shear stress for shear failure n the isotropic plane (output as taucRS)	pressure units	infinite

Notice this law has two axial shear strengths (taucA and taucT). Crack that form by shear are determined by minimum of taucA and taucT. Even though the maximum value is never used to initiate failure, it is still needed for damage evolution. For example, in wood, taucA is called "shear parallel strength," tauT is called "shear perpendicular strength," and tauc is called "rolling shear strength." For wood, tauT is much larger than taucA, which means shear failure is by shear cracks parallel to the wood fibers in the axial direction. But, if the wood initiates failure by tension parallel to the fibers and then is loaded in shear, the shear damage evolution will be determined by softening law based on tauT.